Solve for $x$ : $5\sqrt{x} - 3 = 7\sqrt{x} + 10$
Explanation: Subtract $5\sqrt{x}$ from both sides: $(5\sqrt{x} - 3) - 5\sqrt{x} = (7\sqrt{x} + 10) - 5\sqrt{x}$ $-3 = 2\sqrt{x} + 10$ Subtract $10$ from both sides: $-3 - 10 = (2\sqrt{x} + 10) - 10$ $-13 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{-13}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $-\dfrac{13}{2} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.